Mate who's drunk a bit (8)
I believe the answer is:
somewhat
'a bit' is the definition.
(I've seen this before)
'mate who's drunk' is the wordplay.
'drunk' indicates an anagram.
'mate'+'whos'='matewhos'
'matewhos' anagrammed gives 'SOMEWHAT'.
(Other definitions for somewhat that I've seen before include "To an extent, a little" , "To a certain degree - a bit" , "Moderately" , "up to a point" , "To some degree, sort of" .)